The expression “direct writing” will be used to designate all the techniques wherein the surface of a substrate is locally modified by directing a narrow or shaped particle or photon beam onto it, without making use of a mask. The meaning of this expression is not limited to the case where the substrate is a semiconductor wafer and also includes, inter alia, the writing of photolithography masks.
Electron beam (e-beam) lithography is the most commonly used technique for performing direct writing—or maskless—lithography. It allows achieving a spatial resolution of a few tens of nanometers or less, and is particularly well suited for manufacturing photolithography masks.
FIG. 1 is a schematic illustration of an electron-beam lithography method and apparatus known from prior art. On this figure, reference 11 corresponds to a substrate—e.g. a silicon wafer or a glass or silica plate—onto which a pattern has to be transferred through direct writing (e.g. e-beam) lithography, reference 12 to a resist layer deposed on a surface of said substrate (the term “substrate” will be used indifferently to designate the bare substrate 11 or the ensemble 10 including the resist layer), reference 20 to an electron beam source, reference 21 to an electron beam generated by said source and impinging onto the resist layer 11, reference 30 to an actuation stage for translating the substrate 10 with respect to the electron beam 20, reference 40 to a computer or processor driving the electron beam source 20 and the actuation stage 30, and reference 41 to a computer memory device storing a program executed by said computer or processor 40. The electron beam source 20 and the actuation stage 30 cooperate for selectively exposing to the electron beam specific regions of the substrate, according to a predetermined pattern. Then, during a so-called development step, the exposed (positive resist) or the unexposed (negative resist) is selectively eliminated, so that the remaining resist reproduces the predetermined pattern or its complement on the surface of the substrate. Afterwards, the portion of the surface of the substrate which is not covered by resist can be etched, and then the remaining resist eliminated.
Electron beam 21 may be a narrow circular beam, in which case the pattern is projected onto the resist point by point, using raster or vector scanning. In industrial applications, however, it is often preferred to use “shaped beams”, which are larger and have a rectangular or triangular section. In this case, the pattern to be transferred onto the substrate is decomposed into a plurality of elementary shapes corresponding to the section of the beam. An elementary shape can then be transferred by a single shot—or a series of successive shots for a fixed position of the substrate—with a significant acceleration of the process.
In the real world, the dose actually received by the substrate surface does not fall abruptly at the edges of the beam spot, but it decreases smoothly. Moreover, electrons interacting with the resist and/or the substrate experience forward and backward scattering which broadens the dose distribution beyond the theoretical limits of the incident beam spot; in particular, backscattered electrons can travel by a distance of a few micrometers. The influence of the interactions of primary electrons with the substrate and the resist on the dose distribution is known as “proximity effects”.
On FIG. 2, line 200 illustrates the received dose D distribution across an elementary shape (a line of width W, measured along direction x, and much greater length) of a pattern transferred to a resist layer. The received dose D can be obtained by convolving the emitted dose—which may correspond to the design pattern—with a point-spread function representative of the proximity effects. As a result, the received dose takes a value D0 at the center of the elementary shape, remains approximately constant across a width W0<W and then decreases smoothly. The edges of the transferred elementary shape (line 210) correspond to the point where the received dose D crosses the energy threshold ETh of the resist. Beyond these edges, the received dose does not go to zero, or it does so slowly, mainly because of forward and backward-scattered electrons coming from the considered elementary shape or adjacent ones. It can be easily understood that increasing the emitted dose (dashed line 201, on the left part of the figure) increases the width of the elementary shape, and vice-versa. Moreover, an increase of the contribution from backscattered electrons from adjacent shapes can be compensated by a reduction of the emitted dose (dashed line 203, on the right part of the figure), and vice-versa.
The correction of proximity effects is essential for ensuring an accurate reproduction of the target pattern on the substrate. It requires the development of an accurate physical model including:                An electronic model, commonly referred to as Point Spread Function (PSF, mentioned above), which allows creating an aerial image of the dose on the surface of the sample. Usually the PSF is expressed by the weighted sum of two or more distribution functions, following e.g. a Gaussian law; see FR1157338 and FR1253389. Each basic function of the PSF, characterized by a radius parameter a, is typically used to model the effects within a disk of radius 3σ. For a two-Gaussian PSF, two radiuses are defined, noted α and σb (β is sometimes used instead of σb), corresponding to short range (forward scattering) and long range (backscattering) effects, respectively. A parameter q expresses the relative weight (i.e. the energy ratio) of the two contributions.        A resist model takes into account the response of the resist to the exposition to the electron beam. The simplest example is the “constant threshold” model, defining a constant energy level of the aerial image above which the resist is exposed, and therefore the pattern is printed.        
Once the physical model is calibrated, it is possible to proceed to the stage of correcting, or compensating, the electronic proximity effects (PEC). There are three possible types of correction:                PEC by dose modulation (DM): the exposure dose of each elementary shape of the pattern is adjusted according to the parameters of the physical model.        PEC by geometry modulation (GM): the geometry the elementary shapes of the pattern is modified depending on the settings of the physical model and for a known exposure dose.        PEC by modulation of the dose and geometry (DMG): dose and geometry are simultaneously adjusted for each elementary shape of the pattern.        
The paper by Takayuki Abe et al. “High-Accuracy Proximity Effect Correction for Mask Writing”, Japanese Journal of Applied Physics, Vol. 46, No. 2, 2007, pp. 826-833 describes a commonly used method of performing dose correction modulation. According to the simplest form of this method, the normalized correction dose at a position r=(x,y) of the surface of the sample is given by:
                              D          Abe                =                                            1              2                        +            η                                              1              2                        +                          η              ⁢                              ∫                                                      ∫                    pattern                                    ⁢                                                            g                      ⁡                                              (                                                  r                          -                                                      r                            ′                                                                          )                                                              ·                                          dr                      ′                                                                                                                              (                  eq          .                                          ⁢          1                )            where the integral is computed over the whole pattern to be transferred (or the relevant portion thereof) and the distribution g(r) of the energy deposited by backscattered electron satisfies the normalization condition ∫∫−∞+∞g(r)dr=1.
Typically, g(r) is a Gaussian distribution of standard deviation σb, typically truncated at 3σb, taking into account long-range effects (mainly backscattering):g(r)=A·exp[(−(r−r′)2/σb2)]  (eq. 2)where A is a normalization constant.
If the pattern density is defined by:Density=∫∫patterng(r−r′)·dr′2  (eq. 3)then (eq. 1) can be rewritten in the simpler form:
                              D          Abe                =                                            1              2                        +            η                                              1              2                        +                          η              ·              Density                                                          (                  eq          .                                          ⁢          4                )            
It has been found that dose modulation is simpler to implement than geometry modulation, but less precise. The invention aims at overcoming this drawback of the prior art; more precisely it aims at improving the precision of the received dose modulation on one- and two-dimensional critical shapes (i.e. with narrow width, space or density) without increasing—or even reducing—its implementation complexity.
Document US 2014/077103 describes a method of performing direct writing using a charged particle beam, wherein different dose correction formulas are applied for elementary shapes situated inside the pattern or at its periphery.
Document US 2007/228293 describes a method of performing direct writing using a charged particle beam, wherein a dose correction factor is computed as a function of both a pattern density and of a parameter depending on the shape of the pattern.
More specifically, document JP 2012/212792 describes a method of performing direct writing using a charged particle beam, wherein the dose is computed by taking into account a line width and a pattern density. A “line width” is not easily defined for every kind of pattern.